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  • Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.1 Question 16 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.1 Question 16 Maths Textbook Solution.

Answers (1)

Answer:
                \! \! \! \! \! \! \! \! \! x=2\: or\: 4\\y=4\: or\: 2\\z=-6\\w=4

Given:  \begin{bmatrix} xy &4 \\ z+6&x+y \end{bmatrix}=\begin{bmatrix} 8 &w \\ 0& 6 \end{bmatrix}    

Here we have to find the value of  x,y,z,w

Hint: Here we will use equality of matrices.

Solution:
\begin{bmatrix} xy &4 \\ z+6&x+y \end{bmatrix}=\begin{bmatrix} 8 &w \\ 0& 6 \end{bmatrix}

The corresponding entries of equal matrices are equal, So

xy=8                                                                                                                                              ….. (i)

w=4                                                                                                                                                ….. (ii)

z+6=0                                                                                                                                          ….. (iii)

x+y=6                                                                                                                                          ….. (iv)

From equation (ii) and (iii) we get

z=-6  and w=4

From eqn (iv) we have,

x+y=6\Rightarrow x=6-y   

Substituting the value of x  in eqn (i), we get

\! \! \! \! \! \! \! \! \left ( 6-y \right )y=8\\\Rightarrow y^{2}-6y+8=0\\\Rightarrow \left ( y-2 \right )\left ( y-4 \right )=0\\\Rightarrow y=2 \: or\: 4

Substituting the value of y  in eqn (i), we get

x=4,2
Hence value of x,y,z,w  are  4,2;2,4;-6  and 4 respectively.

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